If jordan? is true, row operations are done both above and below the pivot.
If unitize-pivot? is true, the pivot’s row is scaled so that the pivot value is 1.
When both are true, the algorithm is called Gauss-Jordan elimination, and the result matrix is in
reduced row echelon form.

If pivoting is 'first, the first nonzero entry in the current column is used as the
pivot. If pivoting is 'partial, the largest-magnitude nonzero entry is used, which
improves numerical stability on average when M contains inexact entries.

The first return value is the result of Gaussian elimination.

The second return value is a list of indexes of columns that did not have a nonzero pivot.